Suppose you're creating a site -- let's call it Hacker News -- that requires a user to log in, and all you care about is the part where they enter their username and password.
From there, you're able to assign the user a unique ID and persist their preferences (e.g. header color) across sessions.
It's not exactly a difficult project to roll your own login system, but Anonymous Login gives you the added advantage of being able to "upsell" users into providing more information, if they feel comfortable sharing it.
This would basically make it easier to access or try out all the FB-only-login apps without giving the app owner all the personal info.